Some Research Projects


Insulin Action & Glucose Transport, Insulin-Resistance & Diabetes

David James, University of Sydney
Jerry Greenfield, Dorit Samocha-Bonet, Will Hughes, Garvan Institute of Medical Research, Sydney
Nigel Turner, School of Medical Sciences, UNSW
Cynthia Mastick, University of Nevada, USA
Geoff Holman, University of Bath, UK
Shixiong Tan, Institute of Molecular and Cell Biology, Singapore
Maria Vlasiou, Marko Boon, Stochastic Operations Research, Technical University of Eindhoven, The Netherlands

A breakthrough in the understanding of insulin-regulation of glucose transport came as a direct result of mathematical modelling. Work I undertook with David James found an insulin-dose dependent response in the glucose transport system in adipocytes (fat cells) contrary to the existing dogma. It was previously thought that insulin only controlled the time course of the action rather than the endpoint. This was a novel outcome of my mathematical modelling and would have otherwise not been discovered. This has also opened up a debate within the scientific community about sequestration in insulin-responsive glucose transporter recycling. I followed up this work by showing that that muscle cells also have a differential response to insulin, albeit dissimilar mechanism to adipocytes.

Continuing on, to investigate the key biochemical players and the kinetically distinct steps in the physical translocation of glucose transporter proteins in response to insulin, I have developed new mathematical methods for simultaneous system identification and optimisation, and pinpointed the action of several key biochemical effectors in the system. This involved dynamical systems modelling of the different experimental outputs in terms of the underlying mathematical structure and parameters. I have developed algorithms to simultaneously optimise the mean-field models to all the experimental data and to pinpoint how and where the upstream biochemical components affected the translocation system. The techniques I have developed have already had considerable success, and I am extending the techniques to look at the effect of different genetic mutations on glucose regulation.

At a smaller biophysical scale however, we know that the insulin responsive glucose transporters are embedded in vesicles (small spheres of membrane) for transport. The vesicles then fuse with the destination membrane, and the transporters are released. There is also evidence that the vesicles transit along microtubules suggesting that stochastic queues may be an appropriate model for the response of the system to insulin. I am working with queueing theorists to extend the optimisation and system identification methods I have developed for mean-field models to these stochastic models.

Automated identification of fusion events – image processing

One important technique to obtain data on the translocation of glucose transporters to the cell surface is the analysis of single cell surfaces via total internal reflection fluorescence microscopy (TIRFM). The TIRFM technique produces image sequences of the movements of proteins at the cell surface which can be tracked and modelled as a function of time and cellular treatment. Given the huge complexity of the images and the need for statistical replication, the images need to be analysed in a robust and automatic manner. I derived the mathematical description of the events which were to be identified and then worked closely with a computer scientist to implement this into a software package. This overlaps and has implications for a investigations of actin-tropomyosin interactions as we employ a similar TIRFM system, but utilising single molecule fluorescence.

Clinical studies of insulin-resistance and obesity

At a much larger biophysical scale, I have been able to identify some key features and possible biomarkers of diabetes onset. I analysed patterns in human phosphorylation (activation) and lipidomics data (the structure the constituents of cell membranes). These studies investigated the effect of insulin-resistance and obesity, both independently and in concert. The fact that some subjects could have all the hallmarks of obesity and still remain insulin-sensitive is exciting – what is different about these subjects? I have been able to identify some key features of the different groupings and also correlate these with other markers of metabolism and obesity. We have studied the effects of overfeeding and obesity on these markers of insulin resistance and are conducting a follow up study to further investigate the longitudinal effects.


Cancer virotherapy and immunotherapy

Peter Kim, School of Mathematics & Statistics, University of Sydney
Federico Fascoli, Swinburne University
Chae-Ok Yun, Dept of Bioengineering, Hanyang University, South Korea
Yangjin Kim, Dept of Mathematics, Konkuk University, South Korea

In this collaboration I am modelling the dynamics of cancer progression and the effects of virotherapy, which is a newly emerging treatment strategy. In this treatment, patients are infected with genetically-engineered viruses designed to preferentially attack tumour cells. It is also possible to concurrently apply cancer immunotherapy, which boosts the bodies’ own defences. Experimental data from mouse models is available from collaborators and both mean field and stochastic models are being explored to optimise a model that embodies both the control system as well as all the observed effects with the application of various therapeutic strategies.


The interaction of actin and tropomyosin

Till Böcking, Miro Janco, Faculty of Medicine, UNSW

In this application I have developed techniques to extract data from quantitative single-molecule imaging experiments that can resolve the dynamics of interactions between actin filaments and actin-binding proteins. The actin cytoskeleton plays a critical role in most cellular processes including determination of cell shape, cell adhesion and migration, cytokinesis, membrane function and intracellular transport. This functional specialisation is associated with differences in intracellular localisation, filament organisation, dynamics and interaction with actin-binding proteins. Imaging systems of high temporal and spatial resolution have enabled the collection of some outstanding movies of the interaction of actin and tropomyosin.

However this wealth of data now poses a (good) problem, which is: how can these images and movies be analysed to efficiently and quantitatively extract important features? Furthermore, how can this information then be used to inform and create models to understand the underlying dynamics of the proteins interacting?

I have developed a suite of automated image analysis methods to identify different behaviours, extract kinetic parameters and determine association constants in an unbiased fashion, and inform the mathematical models for the function of the actin cytoskeleton. This builds on my expertise developed in image analysis for cellular glucose transporters. I am comparing simulation studies of the ideal system with experimental results, with implications for the theories of actin decoration and function.


The identification of ancient starch

Judith Field, School of Biology, Earth and Environmental Sciences, UNSW

I have developed a novel system for mathematically identifying the plant species origin of starch grains using mathematical modelling and image analysis of light micrographs. This enables the identification of the food sources ground on ancient stone tools. This work has already created interest in the archaeological community, for instance I enabled the identification of the first known use of nutmeg (Myristica fragrans) by humans; and discovered components of a Neolithic diet in New Guinea.

Starch grains associated with food preparation and consumption are preserved for millennia on the surfaces of stone tools, ceramics and other material culture. The starch grains can be easily extracted but identifying which plant species they come from is problematic. Different archaeological experts use different methods, and identification relies on subjective interpretation. Many grains cannot be identified with any confidence. Geometric and morphological features of each starch grain are determined from a mask of the two-dimensional maximum-projection-area. Fourier analysis of the grain shape, in combination with other geometric and morphological measures, has enabled the creation of effective classifiers to undertake a quantitative evaluation of starch grains, thereby reducing the need for subjective qualitative determination. The system has provided a robust framework in which plant microfossils of unknown species origin can be compared with reference grains for effective identification. I am continually extending the methodology to improve the discrimination by developing other predictive measures and also extend the applicability to other microfossils of morphometric interest.

Current investigations include probing the plant origin of starch grains found on tool artefacts discovered at the Juukan-2 rockshelter, an Aboriginal archaeological site located on the west Hamersley Plateau, in the Pilbara region of Western Australia – recently destroyed by mining exploration.



Electrically Active Cells

The ionic currents underlying the electrical behaviour of neurons and pacemaker cells in the heart may be described using coupled nonlinear differential equations. These have been derived in a number of different models from a wide range of electrophysiological data in the literature. In the cardiac system the dynamics of both single cells and coupled networks of cells is being explored, and the sensitivity of the models to changes in parameters ascertained. Different models for sinoatrial node cells are assessed both analytically and computationally, correlating the different responses with the ionic currents, with a view to further optimising the system.

The normal dynamics of the electrical parameters of cardiac cells forms a stable limit cycle. When a brief current pulse is incident on cells in cardiac and other excitable tissue, a change in phase of the cell’s response is usually observed. There are a number of factors that influence the phase response of the cell. These include the timing of the stimulus, its magnitude, duration and polarity. The particular phase response is dependent on stimulus parameters. So far we have had success in the investigation of synchronisation of cells in the sinoatrial node using highly detailed biophysical models of the cells, both connected directly via gap junctions and also due to proximity.

Explorations are also being made using mathematical models of human myelinated axons that involve coupled differential equations to describe the electrical activity within the nerve. These models are being used to interpret the biophysical mechanisms underlying neural impulse transmission. Extensions to the models are being made to incorporate greater morphological detail in the axonal structure.

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